{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bayesian Statistics Made Simple\n",
    "===\n",
    "\n",
    "Code and exercises from my workshop on Bayesian statistics in Python.\n",
    "\n",
    "Copyright 2016 Allen Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# If we're running on Colab, install empiricaldist\n",
    "# https://pypi.org/project/empiricaldist/\n",
    "\n",
    "import sys\n",
    "IN_COLAB = 'google.colab' in sys.modules\n",
    "\n",
    "if IN_COLAB:\n",
    "    !pip install empiricaldist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import seaborn as sns\n",
    "sns.set_style('white')\n",
    "sns.set_context('talk')\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from empiricaldist import Pmf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Euro problem\n",
    "\n",
    "*\"When spun on edge 250 times, a Belgian one-euro coin came up heads 140 times and tails 110.  'It looks very suspicious to me,' said Barry Blight, a statistics lecturer at the London School of Economics.  'If the coin were unbiased, the chance of getting a result as extreme as that would be less than 7%.' \"*\n",
    "\n",
    "From “The Guardian” quoted by MacKay, *Information Theory, Inference, and Learning Algorithms*.\n",
    "\n",
    "\n",
    "**Exercise 1:**  Write a function called `likelihood_euro` that defines the likelihood function for the Euro problem.  Note that `hypo` is in the range 0 to 100.\n",
    "\n",
    "Here's an outline to get you started."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def likelihood_euro(data, hypo):\n",
    "    \"\"\" Likelihood function for the Euro problem.\n",
    "    \n",
    "    data: string, either 'H' or 'T'\n",
    "    hypo: prob of heads (0-100)\n",
    "    \n",
    "    returns: float probability\n",
    "    \"\"\"\n",
    "    # TODO: fill this in!\n",
    "    return 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "def likelihood_euro(data, hypo):\n",
    "    \"\"\" Likelihood function for the Euro problem.\n",
    "    \n",
    "    data: string, either 'H' or 'T'\n",
    "    hypo: prob of heads (0-100)\n",
    "    \n",
    "    returns: float probability\n",
    "    \"\"\"\n",
    "    x = hypo / 100\n",
    "    if data == 'H':\n",
    "        return x\n",
    "    else:\n",
    "        return 1-x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the prior, we'll start with a uniform distribution from 0 to 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decorate_euro(title):\n",
    "    \"\"\"Labels the axes.\n",
    "    \n",
    "    title: string\n",
    "    \"\"\"\n",
    "    plt.xlabel('Probability of heads')\n",
    "    plt.ylabel('PMF')\n",
    "    plt.title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro = Pmf.from_seq(range(101))\n",
    "euro.plot()\n",
    "decorate_euro('Prior distribution')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can update with a single heads:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro.update(likelihood_euro, 'H')\n",
    "euro.plot()\n",
    "decorate_euro('Posterior distribution, one heads')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another heads:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro.update(likelihood_euro, 'H')\n",
    "euro.plot()\n",
    "decorate_euro('Posterior distribution, two heads')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And a tails:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro.update(likelihood_euro, 'T')\n",
    "euro.plot()\n",
    "decorate_euro('Posterior distribution, HHT')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Starting over, here's what it looks like after 7 heads and 3 tails."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro = Pmf.from_seq(range(101))\n",
    "\n",
    "for outcome in 'HHHHHHHTTT':\n",
    "    euro.update(likelihood_euro, outcome)\n",
    "\n",
    "euro.plot()\n",
    "decorate_euro('Posterior distribution, 7 heads, 3 tails')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The maximum apostiori probability (MAP) is 70%, which is the observed proportion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "70"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euro.max_prob()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the posterior probabilities after 140 heads and 110 tails."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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K/FJEumEO/P/ClivbQF0kIth3+AJmRv8jdd93pDGjqgtCpOHp4YH7MvYgPwPzQ98LEM4djk1obnQeUJZ5BBO2fxKRL2Bm1TMxQdDQxOuI6P48MQj7SYSlrcL1fR37fZ1KnY+rfLNa0nMt5qqYGaJQN2LPjSGkmYsWxzWpPKKq92Pmus8xO/kvsbDY0VEEXXhbPwybp/MdTP0+FXtjGh0LS30W+4EcioWZd1NbqmRv7Ob4X+zhMBR7K0/Oucmkv8sxH9AdmFnjOmze0HnYQ7nZhKitfbE339OweVozaTx6DFWdhjnw12ITIa/D3nKPU9W/xbJeggmV32MPjebyZ0wIXYi9Pb8MfFVVP43l+RXmGP4qpuFFGkMyOOMW7I37/PBJN65XMLv969hD/QqCAFbVlpiRdsZWHziiBWVbjNoE2W9iD7nzsWv0D+yeXZalNqJr9RomYK7GBMtJqvq7WD8OwbSfs7A5e3uFv38O9BZbCw9VfR2LGPwIuw9PCcdklOqp2AM/+r7PxaYI7Kt10wMGYdf9tGyMNVPC8yJaYuk0bBrKJ9h1b3RZMVV9F9N49sZ+L9thY52E3T83hONt1EWZHpBhv57EnmMbsN/kdZjGd4yqNhrJW5RKNTpvz3GcDo6I/AzorqoT8t2XzkQwix+sqm0qqAoN16Qcp4AJYeLHk2YFESd3BD/iyfh1bzUupBynsOkJ/LkB/5eTO0qwpYYaWmPPyRA39zmO4zjtFo/uyxIiUoVppqubyus4juPU0huo0TS7DIMLqWxSDBSVl5f3yXdHHMdxOgoVFRXQiOvJhVT2WF1eXt7ntddey3c/HMdxOgyjRo2ioqKiQQuUB044juM47RYXUo7jOE67xYWU4ziO025xIeU4juO0W1xIOY7jOO0WF1KO4zhOuyXvIehhS+eLsNW55wITVPWODMteA+yhqmMS6b2xlbEPxzaf+whb3fdP0R5AIlKKbYOQ3Ilzrar2wnGcemyorObVj5bx1WED6VLq77dO25DXO01EjgLuwnb1PAzb7vl2ETkyg7JnYMvzp+MebL+Y67DtHB7Dtri4IJZHMAH1A2z7iegzuvkjcZzC53dPfsBJk/7FNdM0311xOhH51qQmAPeq6vjw/9Mi0h/bq2VqugJhl9SrsP2MVqU5vwdwMHC0qt4Xkp8Vkb7Y/jHRdgUjsW2/p8Z3nXQcZ3Oqqmt4+K35ADz81nwu+PYIioub2pfScVpP3jQpERmK7fJ4f+LUVGzb6R0bKPobbOfTMcBbac4XYRvVPZtI/wDoIyIDwv97YLtmuoBynCZ4/ZMVrFhXCcCi1Rt5e/5m74eOkxPyqUmNCMek7WBOOAq2S22Sq4APwtbqlyRPquqbpN8N8zBgIbA8/D8S2CgiT2E7w1ZiO9ueG3aLdRwnMG3Wonr/T5+1kD2265un3jidiXz6pKKFWJNrNkUCone6Qqo6S1VrmtOQiJwF7A/8LgqcwITUMOAJbHvpy4HjgEdFxO0YjhNIpVJMD0Kqdzd7r52eEFqOkyvyqUlFgiC5oVWU3ixB1BAhwOJ6TEu6IXbqGGC5qr4T/p8pIouAOzFT4vRstO84HR1dVMGny80qfsHBO/PLB9/hP4vWMHfpWoYM7Jnn3jmFTj41qciondSYyhPnW4SIFIcQ9RuBu4HjY1oUqvp8TEBFPB6OI1vTtuMUEtPeM61pu/7dOfbL2zGovCvg2pTTNuRTSEW+qOGJ9OGJ881GRMqAKViI+rXACapaFTs/WEROCcEbcbqH49KWtu04hca0WQsBOPCLW1JcXMSYnbeol+44uSRvQkpV52CBEck5UeOA2ar6aSuqvy3UM15Vz41rUIEaYCJwRiL9GKAaeLEVbTtOwTB/5XrenW9u4wO/aMLpwF3s+PonK1i2ZmPe+uZ0DvI9T+oyYJKIrMAm3I4FjsbmQCEig7DghlmqmtG27CJyKHAC8Ajwqoh8JZHlDVVdKiJ/BM4UkdXAC8DXgAuBm4IAdZxOz/T3TFvq37MLe+3QD4CvDhtAzy4lrN1UzbMfLOboUdvls4tOgZPXFSdUdTLwI+Ag4CEsAu9EVZ0SshwKvILNi8qUceE4NpRNfgaH8+cAv8QE4uPYyhOXAGe3aDCOU4C8/OEyAEbLYEpL7HHRtbSE/XYaBMCLs90y7uSWfGtSqOpEzPSW7txkYHIjZfdPk3YycHIG7VZic66uyqynjtP5mLdiPQA7bVF/OUvZspwn313I/JXr89EtpxPhq0Q6jtMgn68yIbR13+710rfuY/8vcCHl5BgXUo7jpGXdpipWhqWQtu5bf7OArcL/C1dvoKo6K1MaHSctLqQcx0nL5ys31P6d1KS2CppUTQoWV3iEn5M7XEg5jpOWBcHUV1JcxODy+ppUXLOK8jlOLnAh5ThOWj4P/qYte3ejJLEtR48upfTpXhbybdisrONkCxdSjuOkJRI+W/VJbl5tRCZA16ScXOJCynGctESaVNIfFbF1EF6uSTm5xIWU4zhpWbAqaFJ902tSUbprUk4ucSHlOE5aIk1qmwY0qSjCzzUpJ5e4kHIcZzNSqVTtahKRMEqytWtSThvgQspxnM1Ysa6SjVU2STc5kTciEl5L12xiY1V1m/XN6Vy4kHIcZzM+jy13tHVDmlQsfeEqN/k5ucGFlOM4mxEJqe5lJfTtUZY2zxZ9usbyu5BycoMLKcdxNiMSUlv17UZRUVHaPF1LS2q3kne/lJMrXEg5jrMZUfh5Q5F9EXVzpVxIObnBhZTjOJtRF9mXPmgiojYM3X1STo5wIeU4zmZEmlRDq01E1E7odU3KyREupBzH2YymlkSKqN380DUpJ0e4kHIcpx5V1TUsWh00qQbCzyMiTcp9Uk6ucCHlOE49FlVspCZlfzc0kTci8kmt3lDF2o1Vue6a0wlxIeU4Tj3i/qWGlkSK8M0PnVzjQspxnHpEkX39e3ahe5eSRvMOLq/bEHG+T+h1coALKcdx6lG7RUcT4edgW8tv2dsj/Jzc4ULKcZx6ZBrZFxEJM58r5eQCF1KO49QjWodv6ww0KYCtom3kXZNycoALKcdx6rFkzUYABvfOUEgFYbZwtWtSTvYpzXcHROQ44CJgKDAXmKCqd2RY9hpgD1Udk0gvBS4BTgIGAK8D56jqPxP5zgJ+CmwDvA9cqKpPtmY8jtPRWRaE1ICeXTLKH+VbvnZTzvrkdF7yqkmJyFHAXcA04DBgBnC7iByZQdkzgHMaOP0H4GzgSuAYoAp4RkSGxsqfB1wLTAaOAD4CHhGRfVo4HMcpCCJhM6BX1yZyGv1dSDk5JN+a1ATgXlUdH/5/WkT6A5cDU9MVEJFtgKuAY4FVac4PAU4DzlDVP4W0acB/gPOAH4tIT+BC4BpVvSLkeQp4GbgYODhbA3ScjsS6TVWs22S77A7olaEmFfItW7OJVCrV4NYejtMS8qZJBa1mGHB/4tRUYISI7NhA0d8AewJjgLfSnD8AKInXq6obgceAQ0LS3kCfRJ4U8AAwRkQy+3U6ToGxbE2dNjSwZ2aa1ICQb1N1DWt81Qkny+TT3DciHDWRPiccpYFyVwG7qOpzjdS7QlWXpKl3exHp3kTbpZh/zHE6HctiJrv+GWpS/WO+Kzf5Odkmn+a+PuG4OpFeEY690xVS1VkZ1JusM15veaztigbypG3bcQqd5WstaKJraTE9m1htIiJuFly2dhM7DOiZk745nZN8alKR4TrVQHpNK+pN1pmsN5M8jtPpWBrMfQN7dc3Yt9SjSyndyuxREjcXOk42yKeQioIeklpLeeJ8S+pNpwlF9a4OeYqAXllu23E6NJGQ6Z9h+HlE5JeKNDHHyRb5FFKRP2h4In144nxL6u0vIv3S1Puxqm5qou2NwCctbNtxOjSRkMk0si+iNsLPfVJOlsmbkFLVOcDHQHJO1Dhgtqp+2sKqp4djbb0i0hU4FHgmJL0MrE3kKcLmS80MgsxxOh2RJjUgw8i+iEjzcnOfk23yPU/qMmCSiKzAQsTHAkdjc6AQkUFYmPosVU0XDLEZqvqJiNwO3CAivYDZ2MTeflhkIKq6LqxW8SsRqQJeBU4G9gL2z97wHKdjsXRt5JNqqbnPhZSTXfIqpFR1ctByzgVOwVZ9OFFVp4QshwKTgNHYahSZchqwArgA8zu9DnwraG8Rv8ZWojgVOB+YBYxV1ZdaPCDH6eBESyI12yfl5j4nR+Rbk0JVJwITGzg3GVu2qKGy+zeQvhEYHz4NlU0BV4SP4zg0f0mkiLqlkTxwwskuvgq64zgApFKpOp9Us8197pNycoMLKcdxAKjYWMWmapsimOmSSBFxc18qlW4KouO0DBdSjuMA9bWgTJdEqs0frd9XVcPasECt42QDF1KO4wD1/UmZ7iWVLn8UfOE42cCFlOM4QN2SSL26ltKtLLN1+yKS6/c5TrZwIeU4DtDyJZGg/vp9yz14wskiLqQcxwFaviRShE/odXKBCynHcYA6c19zl0SKiITbUp8r5WQRF1KO4wB1vqTmLokUUTuh1819ThZxIeU4DtDyJZEi6ladcCHlZA8XUo7jAC1fEiliYCi31IWUk0VcSDmOA8R35W2tJuU+KSd7uJByHIeamhQr1rU8BD1ezn1STjZxIeU4DqvWV1JdY2vutTS6b6Cv3+fkABdSjuOwLGaia7m5z4TbRl+/z8kiLqQcx6n1RwH0a6G5L75+n5v8nGzhQspxnNolkfp0L6OspGWPhbgva5kHTzhZwoWU4zitXhIJoEeXktr1+3zzQydbuJByHKcu/LyFQRMARUVFvn6fk3VcSDmOU2uea2n4eURU3rfrcLKFCynHcWrNc60x98XL+4ReJ1u4kHIcp1bzae6OvElqNSn3STlZwoWU4zi1i8u2dN2+iAFu7nOyjAspx3FqAx1a75PywAknu7iQcpxOTnVNipXrK4HWm/sG+HYdTpYpzXcHROQ44CJgKDAXmKCqdzSSvxdwJTAO6AXMBM5S1dnh/KXAJY00OURVPxGRbYHP0px/T1V3bcFQHKdDsmLdJqKl9vq3MnCinwspJ8vkVUiJyFHAXcAfgKeAw4DbRWSdqk5toNgU4MvAeUAFJpCeE5FdVHUVcGuoK84A4D7gOeoE08hwPAhYHcu7rlWDcpwOxoqYQMlWCPr6ymrWb6qme5eSVtXnOPnWpCYA96rq+PD/0yLSH7gc2ExIici+wCHAwar6VEh7AfgY+BFwparOA+Ylyj0ILAOOV9WakDwSWKSq07I/LMfpOMSDHPr1yI6QAli+bhPbdOneqvocJ28+KREZCgwD7k+cmgqMEJEd0xQ7ENOepkcJqroEeB4TXunaORTT0Mar6srYqT2At1s8AMcpECLTXO9upS1ety8iLqRWuMnPyQL51KRGhKMm0ueEo2AaUrLMHFVN7gMwBzgm2YCIFAFXA8+nMR+OBBaLyIvAKGAVcBtwsapWNmcgjtORWdbKbePj9O5WSmlxEVU1KQ9Dd7JCPqP7+oTj6kR6RTj2bqBMMn9UJl3+/wZ2xsyHtYhID2A4JvT+ivml/gScjfm0HKfTEG2r0Vp/FNj6fVHwhGtSTjbIpyZVFI7JLTyj9Bo2pyhN/ig9Xf4zgDdV9dlEehVmOpyrqh+GtOdFZBNwhYhcEUULOk6hszxL6/ZFDOjZhSUVG12TcrJCPoXUqnBMakDlifPJMkPTpJcn84cAjNHA+cnMqroJSAougMeBKzBToAspp1OQrSWRIqLgC9eknGzQpLlPRHYXkT5N5WsBkS9qeCJ9eOJ8sszQ4GtKlknm/zYmhO9NViIiO4rIqSIyMHEqCkVa2ljHHaeQyNZqExHRXCvXpJxskIlP6k3g0HiCiJSKyH6tEV6qOgcLjDgycWocMFtVP01TbBrQFxgT68sgYD/gmUTer2DmvPlp6ukHTAS+l0g/BvN5vZnhMBynw5N1IdXDV0J3skcm5r6k1gIWwPAc8C3g761o/zJgkoisAB4DxgJHA8dCrQAaBsxS1dWqOlNEZgD3iMj5wHLgUmAlcEui7t2AWekaVdU3ROQR4LciUgK8i4WwnwmcHSYFO06noC66L0tCqjZwwoNkndbTmui+dMKrWajqZGwS7kHAQ8D+wImqOiVkORR4BdgzVtOyWHMAACAASURBVOwI4BHgGmAyNnH3m6q6IlH9FkAyLc73gJuAnwKPYoEUp6rq71s8IMfpYKRSqVrfUf9W7Mobp27jQ9eknNaT7xUnUNWJmOkt3bnJmCCKp60Afhg+jdX7xSbOrwUuCB/H6ZSsXl9FVY0FzGYrcKJWk1rnmpTTenwVdMfpxMS1naz5pGqF1Caqa9LNGHGczHEh5TidmOVZXFw2WU8qBavWuzbltI5MzX0jRGS/2P9RVN/uIlKVroCqzmxVzxzHyTlR0ETPLiV0K8vOiuX1FplduzFrws/pnGQqpC4MnyTXNlLG1+h3nHZObfh5liL7oP5K6ss9ws9pJZkIqV/nvBeO4+SF5VmO7APoUlpMeddSKjZW+Vwpp9U0KaRU1YWU4xQoy9Zkd0mkiP69ugQh5ZqU0zo8cMJxOjHZXlw2on9PX3XCyQ5NalIiclsL6k2p6v+0oJzjOG3IsiwviRRRtzSSa1JO68jEJ3USddtjZLrKRApwIeU47ZwV63IkpFyTcrJEJkLqHWwdvCXAw8ADwLO+e63jdHyyueFhnLqlkXwldKd1NOmTUtWR2B5Ov8N2sn0MWCIid4rIOBHp3mgFjuO0S1KpVNb3koqIrzrhOK0ho3lSqjoXuB64PqxMflj43AVUi8h04EHgkTQLvTqO0w5Zt6majVW2oXW2NaloC/lIU3OcltLs6D5VXaKqf1HVQ4FBmO9pA3ADsEhEnhGRH2e5n47jZJn4kkgDsjhPyuoLQso1KaeVtCoEXVUrVPUeVT0W+Cq2JfsB2BYYjuO0Y+L+omyuOAF1mtSGyhrWbUq7cprjZESrtuoQka9gGxV+F/NX1QDPY3tDOY7Tjoki77qUFtOzS3ZXMRtQb/2+TfTokvddgZwOSrPuHBHpim3d/l3gv4HBwHpgOnAV8KiqLs92Jx3HyT7x1SaKilq9h2k9+iWE1Lb9emS1fqfzkMlk3gHAdzDB9C2gJ7AUi/J7CJimqhty2UnHcbLP8hxN5AUo71pKWUkRldWper4vx2kumWhSi7BJvB8Df8YE04uq6ruZOU4HJpdCqqioiH49urC4YqMLKadVZCKkouCKocDPwgcRaaxMSlXdCO047ZhczZGK6N/ThZTTejIRJLfnvBeO47Q5udimI07d0kgupJyWk8lWHT8EEJEyYJdQZpaqrstx3xzHySG1mlSWw88jXEg52SCjeVIiMh5YDLwO/ANYKiJXi4ib9Byng7K0wkLQc2XuG+BCyskCmUT3nYhtEz8XuAObCzUaODuUH5/D/jmOkwNSqRRL1piQGtw7N+a+fi6knCyQiSZ1OvAq8EVVPUtVxwNfAqYCp4lIbl7DHMfJGas3VLEprNs3qFe3nLQxsJcJv6VrfLsOp+VkIqR2Bu6Mz4UK4efXA13DecdxOhBLKuqmNg4qz40mFdW7pMKFlNNyMhFSPYFVadI/xuZP9c1qjxzHyTmLg+AoKspd4EQkpNZuqmbtRl+/z2kZmc6TSjdxN7rrWrXol4gcB1yEzcOaC0xQ1Tsayd8LuBIYB/QCZgJnqersWJ59gRfSFH9cVb8Ty3cW8FNgG+B94EJVfbI143GcjkCk3fTv0YWyklatM90gg3rVaWhL12ykZ1ePs3KaT27uzgwRkaOwPammYftTzQBuF5EjGyk2BTgK+DlwIiZgnhORPrE8I4G1wD6Jzzmxts/DAkImA0cAHwGPiMg+WRia47RrIiGVK1Nfsm73SzktJdNXmwEisn0irX84Dk5zDlX9NIN6JwD3hmAMgKdFpD9wORaYUY+gIR0CHKyqT4W0FzDT448wDQtMSL2rqq+ma1REegIXAteo6hUh7SngZeBi4OAM+u44HZa2EFLdykoo71ZKxYYq90s5LSZTTer3mCCIf14P5+5Kc+6jpioUkaHAMOD+xKmpwAgR2TFNsQOBCmzVdcA2YcS2Bzkklm8P4O1Gmt8b6BNvOwSDPACM8YhFp9BpCyEVr9+FlNNS8rks0ohw1ET6nHAUTOAly8xR1eo0ZY4BEJFiYFdswvEb4e+FwB+A64IwaqztUsw/9kFzB+Q4HYVojlTOhVSvrny0ZK0LKafFZLwsUg6IfEirE+kV4di7gTLJ/FGZKP9OQHdMyP0SWIJtM3J1yHNJrO2K+tU02rbjFAyLVwch1auNNCn3STktJJ/hNtEua8nIwSi9poEy6SINi2L552M+pbdUdWFI+7uI9AB+LiLXNFFPQ207TsFQt9pEbibyRri5z2kt+RRS0dyrpNZSnjifLDM0TXp5lF9VK4Cn0uR5HDgF07BWYQKpF/W1qcbadpyCoLK6pnapojbTpFxIOS0knyHokT9oeCJ9eOJ8ssxQEUnudT08yi8iu4nIj8Oq7XG6h+PSJtreCHzSdPcdp2MSDwfPtU8qWhrJhZTTUvImpFR1DhYYkZwTNQ6Y3UAI+zRshYsxUYKIDAL2A54JSV8AbmbzMPJjQnufYKHma+NtB8F3BDBTVX1FTKdgiQuMXC0uGxH3SaVSvpm303zyPQX8MmCSiKwAHgPGAkcDx0KtABqG7V+1WlVnisgM4B4ROR9YDlwKrARuCXU+BrwG/EVEBgOfAceHuseF6L51wTf1KxGpwhbQPRnYC9g/14N2nHwSCamupcWU53gViMicWFmdYtX6Svr28NkdTvPI64oTqjoZm4R7EPAQJiBOVNUpIcuhwCvAnrFiRwCPANdgq0XMA76pqitCnZswLeohLJLvYeCLwOGq+mCsnl+H8z/E5kcNBcaq6ktZHqbjtCvic6SKipKW8+wyOGZOdJOf0xLyrUmhqhOBiQ2cm4wJonjaCkywNBgar6pLgdOaaDcFXBE+jtNpiBaXHZxjfxTY7rxFRZBKmZD6whblTRdynBh51aQcx2l72mq1CYDSkuLaHXp9rpTTElxIOU4noy2FFHiEn9M6XEg5TidjcdjwMFc78ibxuVJOa3Ah5TidjLrVJtpGk3Ih5bQGF1KO04lIpVJ15r4crzYR4ev3Oa3BhZTjdCIqNlaxodKWpmwrn9Qg90k5rcCFlON0ItpytYkIN/c5rcGFlON0IuKCYkDPthVSy9dtorLaNxhwmocLKcfpRERCql+PMrqUts3PP5o0nEpRu/q642SKCynH6UQsbuM5UlA/1N1Nfk5zcSHlOJ2IJbVLIrXNHCmA3t1L6VJSXK99x8kUF1KO04lo69UmAIqKijx4wmkxLqQcpxNRu9pEGwopgIE+V8ppIS6kHKcTsaQNV0CP43OlnJbiQspxOhELVpkmNbh32/mkwOdKOS3HhZTjdBJWb6hk1fpKALbr171N23Yh5bQUF1KO00n4bPm62r+369+jTduOzIsLV29o03adjo8LKcfpJMxbsR6A7mUltRsRthXbBs3t85Xrqa5JtWnbTsfGhZTjdBIiTWrbft0pKipq07a37WeaW1VNyrUpp1m4kHKcTkKkSbW1qQ/qNCmob3Z0nKZwIeU4nYR5K0w4tHXQBEC3spJav1QkLB0nE1xIOU4n4bPlJhwi01tbE2lTrkk5zcGFlON0AlKpFJ9FmlT/ttekrF0TjlE/HCcTXEg5TidgxbpK1m2qBvKnSW0X2nVzn9McXEg5Tieg3hypPJv75rm5z2kGLqQcpxMQmdjKu5XSp0dZXvoQmfsWrN7ApirfodfJjNJ8d0BEjgMuAoYCc4EJqnpHI/l7AVcC44BewEzgLFWdHcvTG7gYOBzYEvgIuBn4k6qmQp5SoAJILmK2VlV7ZWVwjtNOqA0/z5MWFW87lYIFq9azw4CeeeuL03HIqyYlIkcBdwHTgMOAGcDtInJkI8WmAEcBPwdOBLYBnhORPrE89wAnAdcBY4HHgJuAC+LNYwLqB8A+sc/oVg7Lcdod8Ym8+WKrvt0oLor6434pJzPyrUlNAO5V1fHh/6dFpD9wOTA1mVlE9gUOAQ5W1adC2gvAx8CPgCtFZA/gYOBoVb0vFH1WRPpigm1CSBsJ1ABTVdWN5E5Bk8+JvBFlJcVs1ac781eu9wg/J2PypkmJyFBgGHB/4tRUYISI7Jim2IGYiW56lKCqS4DnMeEFUAT8GXg2UfYDoI+IDAj/7wF86ALK6Qx8lseJvHF8rpTTXPKpSY0IR02kzwlHwTSkZJk5qlqdpswxAKr6JnBamvYOAxYCy8P/I4GNIvIUsC9QCdwLnKuqFc0biuO0X2pqUrWaVL7CzyO27deDf3y83MPQnYzJp08q8iGtTqRHAqJ3A2WS+aMy6fIDICJnAfsDv4sCJzAhNQx4AtPCLgeOAx4VkbZdfdNxcsjSNRtro+nyae6z9oMm5eY+J0PyqUlFgiC5bn+Uni5GtShN/ig9bUyriJwBXI9pSTfETh0DLFfVd8L/M0VkEXAnMIaYSdFxOjJxgZDPwAmoi/DzwAknU/IppFaFY1IDKk+cT5YZmia9PJlfRIqBq4BzgP8DfhDTolDV59PU83g4jsSFlFMgRAKhf88u9Oya31ipSJNbumYjGyqr6VZWktf+OO2ffJr7Il/U8ET68MT5ZJmhacxxw+P5RaQMC1U/B7gWOEFVq2LnB4vIKSF4I070mrk041E4Tjsnn6ufJ4lrcvPc5OdkQN6ElKrOwQIjknOixgGzVfXTNMWmAX0xcxwAIjII2A94JpbvtlDPeFU9N65BBWqAicAZifRjgGrgxeaNxnHaL/le/TzOFr27UVZi75hu8nMyId/zpC4DJonICmzC7VjgaOBYqBVAw4BZqrpaVWeKyAzgHhE5H4vUuxRYCdwSyhwKnAA8ArwqIl9JtPmGqi4VkT8CZ4rIauAF4GvAhcBNQYA6TkEQ+aS2zdPq53FKiovYpm935i5b55qUkxF5FVKqOllEugLnAqdgyxedqKpTQpZDgUnYKhAzQtoR2EoS12Ca4IvYxN0V4fy4cBwbPkm2A+ZhpsB5wMnYShTzgUswP5bjFAx1c6Tyr0mBaXRzl63jMw9DdzIg35oUqjoRM72lOzcZmJxIWwH8MHzSlTkZEzxNtVuJCSQXSk7BUrGhstasNnRQ+1grrzYM3Sf0Ohngq6A7TgHz/oK6eem7btOnkZxtR+Qb87lSTia4kHKcAuad+TYzY8iAHvTulp8tOpIMCauff7h4LdU16aY9Ok4dLqQcp4B5LwipXdqJFgWwW+jL+spqPlqyJs+9cdo7LqQcp4B593MTUrtu3X6E1Hb9u9Onu2l1b89LN2ffcepwIeU4Bcr6TdXMWWyayq7bNLi0ZZtTVFRUq01F5kjHaQgXUo5ToLy/cDWRy2eXdqRJQV0QhwsppylcSDlOgRL5o7bp253+PbvkuTf12X1bE1KzPl9NVXXataEdB3Ah5TgFy7vzbVebXbZuP6a+iHjwxIdL1ua5N057xoWU4xQotUET7SiyL2Lbft3p28OCJ9zk5zSGCynHKUA2VlXzn0U2kbc9BU1E1AuemLcyz71x2jMupBynAJm9aA2V1RY10R41KcAj/JyMcCHlOAXIu+HBP7i8K4PLu+W5N+mJhNSsBR484TSMCynHKUDasz8qYrcQ4behsoY5vvKE0wAupBynAIki+3Zth5F9Edv07U6/Hr7yhNM4LqQcp8BYvaGSWZ8HIdWONamioiJ227YvUGeedJwkLqQcp8CY9t4iNlXX0K2smK8NH5jv7jTKbiHy0DUppyFcSDlOgfHY258DcMCIwfTsmvd9TRtlj+36ARbht2zNxjz3xmmPuJBynAJixdpNvDh7KQDf2X3rPPemab7+hYGUdy2luibFo//+PN/dcdohLqQcp4CYNmshVTUpenQpYbQMznd3mqRbWQmH7LYVAA++OT/PvXHaIy6kHKeAeOztBQCM2XkLuncpyXNvMuPwPbcB4N/zVvGhh6I7CVxIOU6BsGzNRl7+cBkA39l9qzz3JnP+a0h/tunbHYAH33BtyqmPCynHKRCefHch1TUpyruWst9Og/LdnYwpLi7isC+Z/+zBN+dTE22C5Ti4kHKcgiGK6vvWF7egW1nHMPVFHP6lbQGYv3I9/5q7PM+9cdoTLqQcpwCYoYt59SN7uP/3yPYf1Zdk+OBetRshPvSWm/ycOlxIOU4HZ/WGSn7xwDsA7L1jf77RgUx9cQ7bwwIoHnrzc+Ys9gAKx3Ah5TgdnAlPvM+CVRvoXlbCVUfuTnFxUb671CLG7bUtW/XpxvrKas74vzfYUFmd7y457YC8T0cXkeOAi4ChwFxggqre0Uj+XsCVwDigFzATOEtVZ8fylAKXACcBA4DXgXNU9Z+Jus4CfgpsA7wPXKiqT2ZrbI6Ta16YvYS7//kZAOcdJOwwoGeee9Ry+nQv48bjvsQxf36VDxZW8OtHZzHhiN3y3S0nz+RVkxKRo4C7gGnAYcAM4HYRObKRYlOAo4CfAydiAuY5EYmvpPkH4GxMmB0DVAHPiMjQWNvnAdcCk4EjgI+AR0Rkn2yMzXFyzcz/LGH8lLcA+PKQfpz01SH57VAWGDWkP+ccuBMAd//zUx52/1SnJ9+a1ATgXlUdH/5/WkT6A5cDU5OZRWRf4BDgYFV9KqS9AHwM/Ai4UkSGAKcBZ6jqn0KeacB/gPOAH4tIT+BC4BpVvSLkeQp4GbgYODg3w3Wc1rN+UzUTnnyfO175BIDyrqVcOa7jmvmS/Gi/Yfzjo+U8/58l/GzKW7w4eynnHSQM7t0+N290ckveNKmg1QwD7k+cmgqMEJEd0xQ7EKgApkcJqroEeB4TXgAHACXxelV1I/BYLM/eQJ9EnhTwADBGRLq0eGCOk2U2VdXw2fJ1PPzWfM6e8hb7Xvn3WgE1aod+PHbmvgwd1CvPvcwexcVFXHf0SHbZujepFNz3+jz2v2YGv370PR5/ewHzVqwjlfK5VJ2FfGpSI8JRE+lzwlEwDSlZZo6qJj2qczCzXpRnRRBeyTzbi0j3JtouxfxjH2QyiGxw24sf88LsZHedQqChR2n0jE1B7QO3uiZFdU2KyuoaNlbVsKGympXrKlm2dtNm5ctKihj/rZ04bb9hlBSIBhVnQK+uPHLGvkz512dcO01ZtnYTk16ay6SX5gLQtbSYvj3K6NO9jB5dSikrKaK0uJjSErsWRUVFFAFFDVyawrti+aVvjy6ce5DUrhySTfIppCIf0upEekU4pttStE+a/FGZ3hnkASiPtV3RQJ422860srqGq57+gA2VNW3VpNNB6VZWzD5DB7C/DOabOw9m23498t2lnFJSXMT39t6e74zcitte/JiX5yzjnfmrWF9ZzcaqGhat3sii1b69R3th5LZ9OOlr6QxgrSOfQip6mUm+bEbp6Z7aRWnyR+k1GeSJ6s0kT5tQVlLMLcfvxSsfLWurJp02psG39qLoUERxERQXFVFcXESXkiK6lpbQrayY3t3L2KJ3N7bs3Y2t+naja2nHWkkiG/TuVsbPxuzEz8ZAVXUNsxevYcGq9axcV8nKdZWsr6ymqjpFVU0NVTUpUilIkWpQjXVDYfbp26OMw/fcNid151NIRVtxJrWW8sT5ZJmhadLLY/lXpakzXu/qkKcIC2GvSJOnTbcJHT1iMKNHtP9tFRwn35SWFLPzVr3Zeas2M3Y4eSafIeiRP2h4In144nyyzFARSb6cDo/lV6C/iPRLk+djVd3URNsbgU+a7r7jOI6Ta/ImpFR1DhYYkZwTNQ6Yraqfpik2DegLjIkSRGQQsB/wTEiKIv+OjOXpChway/MysDaRpwibLzUzCDLHcRwnz+R7ntRlwCQRWYGFiI8FjgaOhVoBNAyYpaqrVXWmiMwA7hGR84HlwKXASuAWAFX9RERuB24Iq1PMxib29gOuCnnWicg1wK9EpAp4FTgZ2AvYvw3G7TiO42RAXoWUqk4OWs65wCnYqg8nquqUkOVQYBIwGluNAkzbuQ64BtMEXwSOVtUVsapPA1YAF2B+p9eBbwXtLeLX2EoUpwLnA7OAsar6UpaH6TiO47SQIp8Ulx1EZGV5eXmf1157Ld9dcRzH6TCMGjWKioqKVaraN915XwXdcRzHabfk2ydVSPSuqKhg1KhR+e6H4zhOh6GiogIaWUDBhVT2qAGKKyoq0q124TiO46SnN40soOA+KcdxHKfd4j4px3Ecp93iQspxHMdpt7iQchzHcdotLqQcx3GcdosLKcdxHKfd4kLKcRzHabe4kHIcx3HaLS6kHMdxnHaLCynHcRyn3eJCynEcx2m3uJByHMdx2i2+wGyeEZHjgIuAocBcYIKq3pHXTmUJESnGNpU8HRvfIuBh4BJVrQh5RmEbWI4CVgOTw/nKfPQ524jIA8Duqjo8lnYg8BtgF+ya3KSq1+api1lBRPYDfgvsie2UfT/wC1VdE84X4ph/BJwFbA98CFypqnfFzhfEmEVkD+BfwI6qOi+W3uT4svH7dk0qj4jIUcBdwDTgMGz34dtF5Mh89iuLnA/cBDyOje9a4AfAfQAiMhx4FlgPHB3Onw1cn4/OZhsROQE4PJH2VeAx4ANsl+m7gKtF5Ny272F2EJGvANOBhcBY4DLgBODWcL4Qx3wqcAt2b38XeAa4M/ymC2bMIiLYOEoT6U2OL1u/b18FPY+IyBzgNVU9NpY2BXvz3jl/PWs9IlIELAPuVtWfxNKPAe4BvgScARwIDFfVTeH8j4EbgR1UdX6bdzxLiMjWwLvAWmBjpEmJyDNAL1X9SizvlZjGuaWqbsxHf1uDiDwf/txfVVMh7SfYA2k34BEKb8wvAxtU9YBY2kygWlVHd/TvWURKsb7+DqgE+gPbRZpUJuMTkVvJwu/bNak8ISJDgWGYWSTOVGCEiOzY9r3KKuXAncD/JdI/CMdh2A38aHQDB6YCJeFcR+ZWTEN+NkoQkW7AfqT/zvsCX22z3mUJERkIfB24JRJQAKr6R1Udhu0TVFBjDnQDKhJpy4ABBfI97wtchWk/P4+faMb4svL7dp9U/hgRjppInxOOAnzcdt3JLqq6GjgzzanDwvF9YDsS41fVJSKyGht/h0RETgH2wmz118RODQXKaPw7fy7nHcwuuwFFwPJgBfgOUIW9nJwN7EjhjRngD8Bfgnnvaeyh+x3glxTG9/w+MFRVF4vISYlzTY5PRP5Bln7frknljz7hmNzJN3o7a3A75Y6KiOwNXAA8BKwIyel2Mq6gg45fRHYArgNOV9WlidOF+J0PCsfJwFLgv4FLgRMxn00hjhng7vC5F1iF+VnvUtWrKYAxq+oiVV3cwOlMxtdQnihfxtfANan8URSOSadglN7gdsodERH5GuZo/Rg4BegaTqVzihbRAccf/HC3AU+oatIUAg1/5xEdbsxAl3B8OeZ7/Hu4FtcAfw5phTRmMD/bVzFt8Q1gb+DioCXcE/IU2pgjMrmPG8vTrN+3C6n8sSock28U5YnzHZ4QLDEZ+A/wbVVdJiK9wul0b1S96Jjj/wmwO7BbcDxD+LGG/xv6zqP/O+KYo7fnJxLpT2P+jC+H/wtmzCGy7SDgh6o6OSQ/LyIrgYnAX0NawYw5QSb38eoG8kAzf99u7ssfka12eCJ9eOJ8h0ZEzsbMIq8A+6nqAoAwf2Y+ifGLyGDsxu6I4z8SGAgswCKiKjGz17Dw99eBagrrO58djl0T6ZGG9TGFN+YdwvGlRPrMcNyDwhtznA9pYnzZ/H27kMoTqjoH+wEn50SNA2ar6qdt36vsIiL/g71N34tpUMm3p2nAf4tIl1jaOOwHMKNNOpldTsM0h/jnMWBe+Ps+7EF2RDCHRYzD3ixfa9PeZof3gU+AYxPpUQDFKxTemKMH7H6J9H3C8QMKb8y1qOoGMhtfVn7fPk8qj4SomUnAH7GH2Vjgx8Cxqjolj11rNeGN6WNgCTaxsyqRZQ6mdbyJvZH+HtgJW7XgNlU9ve16mztEZDKwb2ye1AHYxM/7MBPoV4ELgQtU9ao8dbNVBHPu3VhE32QssvEybAWCcwp0zA8CY4CLsXt4VPj7RVU9pJDGHHtOxedJNTk+ERlBFn7frknlkWDP/hFm334I2B84saMLqMC3gR6YaeQF7I06/vm2qn6Ahe72wuZPnI1Fxp2Vjw63Bar6d+xtcmfsOz8eOK+jPbjihPv1COCL2MvWTzAhdV44X3BjxjTHG4HxwFNYMNA1hBVGCnTMtWQyvmz9vl2TchzHcdotrkk5juM47RYXUo7jOE67xYWU4ziO025xIeU4juO0W1xIOY7jOO0WF1KO4zhOu8XX7nM6FGFy7A8SyTXY5oLvAzer6u1ZbG8uMFdV92/L+kRkBjBEVYc08P9k4AeqWhQr0wUY1JabRYrIGGy+0FDgn6r69TR5LgUuwbYfn9tWfWuI9tYfp3FcSDkdlfHY1hBgi7j2wVa2mCwiA1X12rz1LDv8BujZyPmJ2Ix/oHaLkGnABGwFgJwjIsXYKhPV2Pcxry3adToXLqScjspDybdgEfkrMAvbMuGm9r5Fd2Oo6vQmzkcrd0TsiC0705Zsie0ndZ2q3tzGbTudBPdJOQWDqq4HHsVWWd4lz93pDEQLhya3UXecrOGalFNoRJuplUKtD2g69kJ2PGYi/FLYxvrrmG/iK6HMP4FLVXUmCcKK7hcCWwP/Bi5W1adj54uwVdBPxtYzKwPmYgtzXqWqqWbWN4OYDypNfyYTfFKxBUABJonIJGAEthr31ap6fqLslcDPgC1VdQVpEJEBwOXAd7GFgKOxXK2q1TG/DsAlInIJMFpVZ6SrLzBcRG4ERgObsI0Dz1bV5bF2+2Hr/h0R2v0I+BNwQ/waisie2PXbF+iP7fT8DHB+tAhqyDcMuAo4ADNLTmTzxY4RkR8Bp2NbS6zHVvm+SFXfa2Q8ThvgmpRTMAQfyf7ARszsF3EctsfPWcBfgoAai20XsD32ML48/P1sOBdnFBYcMAX4JdAXeDwEDURcjm2XPgtbSPOXwAbgd9ieUs2trznMxFaXBtsJ9/uqqtiOsUelyX808FQjAqof8DLwP9jCCSxRmwAABlJJREFUoOOxoJQJmA8K4IGQDvAg8P2QpzEexrSuszGN9wfYTsZRuz3DWL4P3I4J0nexFbRviuXbDXgREygTsAVtn8QWff1bLN8WYRwHANcDVwLfI7HAqYgcj313b4Zz1wJfA2aISB+cvOKalNNR6Scia8LfpcAQ7KE5Erg+bLoW0R04WlU/hNpdcv+Ibco2SlVXh/SJ2EPxZhF5UlUrQ/mewKGq+kTINxnb7O9KYC8RKQN+CtyjqidFjYrIrcBibLXoeMRho/U190Ko6kciMh0TeK+o6p3h1F3AtSLyX6r6z9DWPuFaXdBIlT/H/FuHq+pDIe1mEfkjcLqITFbVJ8NW6dcDb8fabIxbVTUSEH8Wke2AQ0Ska/AfnhfaHaWq74R8t4jIb4FfiMifVfXfmMaTwjS35bH6ugDHikj/kH4e5jMbpapvhPHfjn3HcY4H3lPV2qhREXkLuBrYlc03N3TaENeknI7KG9heVUuwnXBfwUxTN7L5A3hOJKACewLbYvsdRdtco6orsTf2bTBtJ+K9SKCEfMuBO4E9RWTLIMy2AE5NtDsQ20a7VyK90foyGHum3IOZP4+OpR0LrME0mYYYC7wfE1ARl4fjYS3sz92J//+FmUUHhP/HYQJkgYgMjD7YVhBgGymCCakhCTNhb0xzhbrrfTDwr0hAAajq4jT9mAeMEJFLRGRIyPeEqu6iqi6g8oxrUk5H5QRgUfi7GliJPVg3pMm7OPH/juGYbgvryGS1A3XRcx+kyRcJvSHAQszHcqiIfBcQ4AtAv5An+TKYSX2tRlU/F5Hnsd2fzw3m0KOAh1V1XSNFd8T2SErWt1BEVlK3fXpzSX4P68MxCsAYhmm9Sxoov33oR0pEBojIL4DdQ7kdsKkIUHe9h2AmxiTJ638ZtqvupcClIjIL85fdmni5cfKACymno/JSMyZiVif+L0qby4gecJtiaek2XYvyVYegiTsx39eLmB9kIuZf+Xuaso3W10jfWsJdwK0isjcmALZic00iSVPXZ1Mj5xujponzJdj1+3UD5z8HEJFDMeHzOXZ9n8S2LD8I+EUsfwrolqaeei8NqjpPREZiAR3fxTbsvAA4W0QOVNXnm+i3k0NcSDmdkbnhOILN37QlHD+LpQ1JU8cXwvEj4OuYgLpcVS+urch8XwNCnjhN1ZdN7sf8b2OxnZKXYZN+G2Mudm3qEUyRval/bbLJXKBcVZ+JJ4ZAjm9ifjswk+5szNe0Npbv+ER9H5F+7tjQRP27Aajqs8CzIe1rwHPAmYALqTziPimnM/I65sc6PfgygFq/xunh3Oux/HuJyJdi+bbAzI0vqOoy6nwq8YhCgP/FBEPyZbCp+lpCpIEltYSVwBPAIeEzNRYQ0hCPYj6apO8p8vU91sI+NsUjwMigKcW5CLgPC2IAu96fJATUdljYOtRd7weAXUTk27F8fbDowTj3AX8TkZJY2puYxphtzdZpJq5JOZ0OVa0UkZ8C9wKvhSg8gFOweUtHqmrcNLUceFpErsPm2PwEc/hHIdgvYwES14vI9ph/bDRwDObML090oan6WkLkxzkhmB9vV9VoPtD/YQ9iMMHZFBOwIIYpInIL8B9MkzkCeEBVn2xFPzNp9wER+RPwHjYP6vuYSS9q90ngmJDnX5hm9L/8fzt3yxJBFEZx/IjBYjca7xewCwrCdoPFLIJNxCSKFkFcxCAILixWX4oGu8Vi9wkigsVi8QOs4Yzsi8LOiriX8f+rA3fu7IZn7tzz3PYxUp+/975c/C9TSgfyntiSvn7O3JN0IrcfnBXXF+VPhZykMWSspPAvRcSFpDl5X2NTjm8/ybHm3lTbjXyW3oqccHuWNB0R98VYr/Iq5VHShtyzNCkn6Y7kt/mJsuP98Hke5M9gU3JfUWe44Vouoi+SbkuM9SYHCU6LZ6jLDcpr6k4K/qqO+zblgMeh3Gi9o+4Xh2VJDbXTnPPFXGeL6zPFeO9ykTuXi9OWvE+43XPfhtyzNS7/d7tyqKPWpzkZf2Ck1fpuDxdAVaSUxuQk5HFErA97PsAgWEkB1bcgnxLfHPI8gIGxJwVUVEppVT7epybpKiL6HVsEZIeVFFBdo3Lv0J3KBSaA7LAnBQDIFispAEC2KFIAgGxRpAAA2aJIAQCyRZECAGSLIgUAyNYHLUqq3rPIyPIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro = Pmf.from_seq(range(101))\n",
    "\n",
    "evidence = 'H' * 140 + 'T' * 110\n",
    "for outcome in evidence:\n",
    "    euro.update(likelihood_euro, outcome)\n",
    "    \n",
    "euro.plot()\n",
    "\n",
    "decorate_euro('Posterior distribution, 140 heads, 110 tails')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior mean is about 56%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "55.95238095238095"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euro.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So is the MAP."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "56"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euro.max_prob()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the median (50th percentile)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(56.)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euro.quantile(0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior credible interval has a 90% chance of containing the true value (provided that the prior distribution truly represents our background knowledge)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([51., 61.])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euro.credible_interval(0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Swamping the prior\n",
    "\n",
    "The following function makes a Euro object with a triangle prior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def TrianglePrior():\n",
    "    \"\"\"Makes a Suite with a triangular prior.\n",
    "    \"\"\"\n",
    "    suite = Pmf(name='triangle')\n",
    "    for x in range(0, 51):\n",
    "        suite[x] = x\n",
    "    for x in range(51, 101):\n",
    "        suite[x] = 100-x \n",
    "    suite.normalize()\n",
    "    return suite"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's what it looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro1 = Pmf.from_seq(range(101), name='uniform')\n",
    "euro1.plot()\n",
    "\n",
    "euro2 = TrianglePrior()\n",
    "euro2.plot()\n",
    "\n",
    "plt.legend()\n",
    "decorate_euro('Prior distributions')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 9:** Update `euro1` and `euro2` with the same data we used before (140 heads and 110 tails) and plot the posteriors.  How big is the difference in the means?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(55.95238095238095, 55.74349943859505)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "evidence = 'H' * 140 + 'T' * 110\n",
    "for outcome in evidence:\n",
    "    euro1.update(likelihood_euro, outcome)\n",
    "    euro2.update(likelihood_euro, outcome)\n",
    "\n",
    "euro1.plot()\n",
    "euro2.plot()\n",
    "\n",
    "decorate_euro('Posterior distributions')\n",
    "plt.legend()\n",
    "\n",
    "euro1.mean(), euro2.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior distributions are not identical, but with this data, they converge to the point where there is no practical difference, for most purposes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
